Calculation method of equivalent elastic modulus of composite structure of ultra-thin silicon steel core and insulating paint
Patent Information
- Application Number
- CN202611234473.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-14
- Publication Date
- 2026-10-30
AI Technical Summary
此外，铁心与绝缘漆之间的界面并非理想结合，存在微观形貌起伏、结合面积不足以及潜在的微损伤，这种复杂的界面效应极大地影响了载荷传递与整体刚度，但现有方法缺乏有效的参数对其进行量化与纳入计算模型
[0016]本发明技术效果：本发明公开了超薄硅钢铁心与绝缘漆复合结构的等效弹性模量计算方法，通过分别计算并修正铁心基体、环氧树脂层及界面过渡层的等效弹性模量，并依据实际载荷方向进行串联或并联组合，实现了对超薄硅钢铁心与绝缘漆复合结构等效弹性模量的精确计算。该方法有效克服了传统方法忽略材料正交各向异性、固化收缩效应及界面损伤的缺陷，使得计算结果能够更真实地反映复合结构在实际工况下的宏观力学行为。由此获得的准确等效弹性模量参数，为电力变压器铁心的振动特性分析、减振降噪的优化设计提供了可靠的力学依据，有助于从源头抑制变压器运行噪声。
Smart Images
Figure CN123017295A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of mechanical property analysis technology of ferromagnetic composite materials, and particularly relates to a method for calculating the equivalent elastic modulus of an ultrathin silicon steel core and insulating varnish composite structure. Background Technology
[0002] Power transformers, widely used electrical equipment in power systems, primarily function to convert AC voltage, greatly facilitating power transmission, especially in ultra-high voltage substations where their application is particularly significant. However, during operation, power transformers inevitably generate vibrations, leading to noise pollution in the surrounding environment and seriously impacting the study, work, and even physical and mental health of nearby residents. In the field of power equipment, the key to reducing transformer vibration noise lies in optimizing the core assembly process and thoroughly analyzing its mechanical properties. The elastic modulus, as a core parameter measuring a material's resistance to deformation during the elastic deformation stage, has a crucial influence on the core's vibration characteristics. Notably, the unique laminated structure of the core and the shrinkage stress generated by epoxy resin curing significantly alter the macroscopic mechanical properties of the composite material.
[0003] However, existing equivalent analysis methods, such as the hybrid law method and finite element homogenization, have significant limitations when analyzing the mechanical properties of composite structures composed of ultrathin silicon steel cores and insulating varnish. These methods often fail to adequately consider interface effects, material anisotropy, and non-uniform distribution characteristics, leading to large discrepancies between calculated results and actual measurements, and making it difficult to accurately reflect the true mechanical behavior of the material. Specifically, in the actual operating conditions of transformer cores, silicon steel sheets exhibit significant orthotropic anisotropy during the rolling process, with their elastic modulus varying in different directions. Simplifying this to isotropic in traditional methods introduces errors. Simultaneously, the shrinkage strain generated during the curing process of epoxy resin insulating varnish creates residual stress, altering its own mechanical state and the mechanical state of the area bonded to the core—a factor often ignored in traditional models. Furthermore, the interface between the core and the insulating varnish is not ideally bonded, exhibiting microscopic morphological fluctuations, insufficient bonding area, and potential micro-damage. This complex interface effect significantly impacts load transfer and overall stiffness, but existing methods lack effective parameters to quantify and incorporate these effects into the calculation model.
[0004] Because the aforementioned interface effects, material anisotropy, and non-uniformity are not fully considered, the equivalent elastic modulus calculated using traditional methods is insufficient to accurately predict the vibration response of transformer cores under magnetostrictive excitation, thus hindering the precise design and optimization of vibration reduction and noise reduction measures. Therefore, there is an urgent need for a more accurate method for calculating the equivalent elastic modulus of ultra-thin silicon steel core and insulating varnish composite structures that can comprehensively consider the influence of the above-mentioned multiple factors. Summary of the Invention
[0005] To address the aforementioned technical problems, this invention proposes a method for calculating the equivalent elastic modulus of an ultra-thin silicon steel core and insulating varnish composite structure. This method enables accurate calculation of the equivalent elastic modulus of the painted silicon steel core, providing key mechanical parameters for vibration reduction and noise reduction design of transformer cores.
[0006] To achieve the above objectives, this invention provides a method for calculating the equivalent elastic modulus of an ultrathin silicon steel core and insulating varnish composite structure, including: S1. Obtain the equivalent elastic modulus of the iron core matrix; S2. Obtain the equivalent elastic modulus of the epoxy resin insulating varnish layer; S3. Obtain the equivalent elastic modulus of the interface transition layer between the iron core matrix and the epoxy resin insulating varnish layer. S4. Based on the equivalent elastic modulus of the core matrix, the epoxy resin insulating varnish layer and the interface transition layer, the overall equivalent elastic modulus of the composite structure is calculated through a mechanical combination model.
[0007] Optionally, obtaining the equivalent elastic modulus of the core matrix in step S1 includes: Based on the orthogonal anisotropy of the core matrix, its compliance coefficient is established; X-ray diffraction is used to obtain the grain orientation data of the silicon steel sheet and calculate the orientation distribution function; the Voigt-Reuss-Hill averaging method is used, combined with the orientation distribution function, to calculate the equivalent elastic modulus of the core matrix in the rolling direction and transverse direction, and its orthogonal anisotropic elastic modulus tensor is constructed.
[0008] Optionally, obtaining the equivalent elastic modulus of the epoxy resin insulating varnish layer in step S2 includes: The initial elastic modulus of the epoxy resin insulating varnish in the glassy state was obtained through dynamic mechanical analysis; its curing shrinkage strain was measured through thermomechanical analysis; based on the initial elastic modulus and the curing shrinkage strain, the Voigt-Reuss-Hill model was modified to obtain the modified equivalent elastic modulus of the epoxy resin layer.
[0009] Optionally, obtaining the equivalent elastic modulus of the interface transition layer between the core substrate and the epoxy resin insulating varnish layer in step S3 includes: The actual bonding area ratio of the interface transition layer and the local elastic modulus obtained by nanoindentation test are obtained; the interface bonding strength data are obtained by shear test, and the interface damage factor is obtained by fitting based on the data; the effective elastic modulus of the interface transition layer is calculated using the actual bonding area ratio, the local elastic modulus and the interface damage factor.
[0010] Optionally, the mechanical combination model in S4 is a parallel model; calculating the overall equivalent elastic modulus through the mechanical combination model includes: considering the iron core matrix, the interface transition layer and the epoxy resin insulating varnish layer as parallel spring units; and calculating the transverse equivalent elastic modulus of the composite structure based on the equivalent elastic modulus and volume fraction of each layer according to the principle of parallel stiffness superposition.
[0011] Optionally, the stiffness of the parallel spring unit is determined based on the equivalent elastic modulus, cross-sectional area, and length of each layer.
[0012] Optionally, the mechanical combination model in S4 is a series model; calculating the overall equivalent elastic modulus through the mechanical combination model includes: considering the iron core matrix, the interface transition layer and the epoxy resin insulating varnish layer as series spring units; and calculating the longitudinal equivalent elastic modulus of the composite structure based on the equivalent elastic modulus and volume fraction of each layer according to the principle of series stiffness synthesis.
[0013] Optionally, the stiffness of the series spring unit is determined based on the equivalent elastic modulus, cross-sectional area, and length of each layer.
[0014] An electronic device, the electronic device comprising: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure.
[0015] A computer storage medium storing computer program instructions, which, when executed by a processor, implement a method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure.
[0016] Technical advantages of this invention: This invention discloses a method for calculating the equivalent elastic modulus of an ultra-thin silicon steel core and insulating varnish composite structure. By calculating and correcting the equivalent elastic modulus of the core matrix, epoxy resin layer, and interface transition layer separately, and combining them in series or parallel according to the actual load direction, the method achieves accurate calculation of the equivalent elastic modulus of the ultra-thin silicon steel core and insulating varnish composite structure. This method effectively overcomes the shortcomings of traditional methods that ignore material orthogonal anisotropy, curing shrinkage effect, and interface damage, enabling the calculation results to more realistically reflect the macroscopic mechanical behavior of the composite structure under actual working conditions. The accurate equivalent elastic modulus parameters obtained thus provide a reliable mechanical basis for the vibration characteristic analysis and vibration reduction and noise reduction optimization design of power transformer cores, helping to suppress transformer operating noise from the source. Attached Figure Description
[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure according to an embodiment of the present invention. Figure 2 This is a schematic diagram of grain orientation represented by Euler angles in an embodiment of the present invention; Figure 3 This is a schematic diagram of the thermomechanical analysis temperature spectrum of epoxy resin in an embodiment of the present invention; Figure 4 This is a schematic diagram of the parallel and series combination of the composite structure according to an embodiment of the present invention. Detailed Implementation
[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.
[0020] like Figure 1 As shown, this embodiment provides a method for calculating the equivalent elastic modulus of an ultrathin silicon steel core and insulating varnish composite structure, including: S1. Obtain the equivalent elastic modulus of the iron core matrix; S2. Obtain the equivalent elastic modulus of the epoxy resin insulating varnish layer; S3. Obtain the equivalent elastic modulus of the interface transition layer between the iron core matrix and the epoxy resin insulating varnish layer. S4. Based on the equivalent elastic modulus of the core matrix, the epoxy resin insulating varnish layer and the interface transition layer, the overall equivalent elastic modulus of the composite structure is calculated through a mechanical combination model.
[0021] Furthermore, obtaining the equivalent elastic modulus of the core matrix in S1 includes: Based on the orthogonal anisotropy of the core matrix, its compliance coefficient is established; X-ray diffraction is used to obtain the grain orientation data of the silicon steel sheet and calculate the orientation distribution function; the Voigt-Reuss-Hill averaging method is used, combined with the orientation distribution function, to calculate the equivalent elastic modulus of the core matrix in the rolling direction and transverse direction, and its orthogonal anisotropic elastic modulus tensor is constructed.
[0022] Specifically, the implementation process of this embodiment includes: The equivalent elastic modulus of polycrystalline materials was calculated using the Voigt-Reuss-Hill averaging method combined with ODF data. Considering the significant orthotropic mechanical properties of oriented ultrathin silicon steel sheets during the rolling process, i.e., differences in their elastic modulus along the rolling direction (RD), transverse direction (TD), and normal direction (ND), their elastic constants vary independently in different directions. For single-crystal silicon steel, their elastic constants were assumed based on empirical measurements. c 11 =230GPa, c 12 =135GPa, c 44 =116GPa, further constructing the compliance coefficient: (1); In the formula s 11 , s 12 , s 44 All values are compliance coefficients. Unpainted grain-oriented silicon steel sheets were cut and sampled, and their pole figure scans were performed using an XRD diffractometer. The diffraction intensity distributions of the {110} and {200} crystal planes at different orientations were collected. The scan data were imported into the MATLAB toolbox MTEX, and the Euler angles were calculated using the harmonic function expansion method. g =( Orientation distribution functions along the rolling direction and perpendicular to the rolling direction f 1(g) and f 2(g) and texture coefficient W 1 and W 2, of which Let the rotation angles of the Gaussian texture about the reference grain's own normals RD, TD, and ND be as follows: Figure 2 As shown. The polycrystalline elastic modulus is further solved using first-principles calculations. According to the Voigt-Reuss-Hill method, for anisotropic elastic bodies, the following equation holds: (2); In the formula, E Voigt and E Reuss These are the constant strain elastic modulus and the constant stress elastic modulus, respectively. E Hill This is the average elastic modulus.
[0023] Furthermore, obtaining the equivalent elastic modulus of the epoxy resin insulating varnish layer in step S2 includes: The initial elastic modulus of the epoxy resin insulating varnish in the glassy state was obtained through dynamic mechanical analysis; its curing shrinkage strain was measured through thermomechanical analysis; based on the initial elastic modulus and the curing shrinkage strain, the Voigt-Reuss-Hill model was modified to obtain the modified equivalent elastic modulus of the epoxy resin layer.
[0024] Specifically, the implementation process of this embodiment includes: The equivalent elastic modulus in each direction is calculated based on the texture coefficient and orientation distribution function in the rolling direction and perpendicular to the rolling direction. E RD and E TD The equivalent elastic modulus tensor of the orthotropic iron core is further corrected as follows: (3); Considering the isotropic nature of the epoxy resin layer and the influence of residual stress on the elastic modulus due to shrinkage during the curing process, the storage modulus of the epoxy resin insulating varnish sample in the glassy region was recorded using a dynamic mechanical analysis device. E ′, i.e., initial elastic modulus E DMA ,refer to Figure 3 As shown. The curing shrinkage strain Δ of epoxy resin as it cools from the curing temperature to room temperature was measured using a thermomechanical analyzer. ε curing The experimentally measured initial elastic modulus and curing shrinkage strain were introduced into the Voigt-Reuss-Hill model to correct it as follows: (4); in, E epoxy The equivalent elastic modulus of epoxy resin is expressed as the volume fraction of epoxy resin. V epoxy =1, ν Poisson's ratio for epoxy resin.
[0025] Furthermore, obtaining the equivalent elastic modulus of the interface transition layer between the core matrix and the epoxy resin insulating varnish layer in step S3 includes: The actual bonding area ratio of the interface transition layer and the local elastic modulus obtained by nanoindentation test are obtained; the interface bonding strength data are obtained by shear test, and the interface damage factor is obtained by fitting based on the data; the effective elastic modulus of the interface transition layer is calculated using the actual bonding area ratio, the local elastic modulus and the interface damage factor.
[0026] Specifically, the implementation process of this embodiment includes: Scanning electron microscopy or atomic force microscopy is used to scan the cut interface layer sample to obtain the actual bonding area ratio of the interface region. A contact / A total The local elastic modulus of the interfacial transition region was measured using a nanoindenter. E AFM Shear loading tests were conducted to obtain bonding strength data at different locations, and the critical shear stress at the interface debonding was recorded. τ critical And shape parameters reflecting the data dispersion are obtained by fitting the experimental data. k and the scale parameter of the characteristic intensity of the reaction λ Further, damage factors were obtained. β =1-e -(τcritical / λ)k Thus, the effective elastic modulus of the interface is determined. E interface Correction: (5).
[0027] Furthermore, the mechanical combination model in S4 is a parallel model; calculating the overall equivalent elastic modulus through the mechanical combination model includes: considering the iron core matrix, the interface transition layer, and the epoxy resin insulating varnish layer as parallel spring units; and calculating the transverse equivalent elastic modulus of the composite structure based on the equivalent elastic modulus and volume fraction of each layer, according to the principle of parallel stiffness superposition. The stiffness of the parallel spring unit is determined based on the equivalent elastic modulus, cross-sectional area, and length of each layer.
[0028] Specifically, the implementation process of this embodiment includes: Considering the actual operation of transformer cores, the vibrations generated by magnetostriction are mainly distributed parallel to the interlayer distribution. For the core-interface-epoxy resin composite structure, each layer shares the load; therefore, it can be considered a parallel model, such as... Figure 4 As shown, the equivalent parallel stiffness of the composite structure is: (6); in, k eq,parallel For the equivalent parallel stiffness of the composite structure, k core , k interface , k epoxy This represents the equivalent stiffness of the core, interface layer, and epoxy resin. Spring stiffness of each layer. k i = E i · A i / L i In the formula A i and L i Given the cross-sectional area and length of each layer, and assuming that the epoxy resin insulating varnish is completely coated on the core surface, the volume fraction of each layer is... V i = A i / A total Therefore, the transverse equivalent elastic modulus of the core-interface-epoxy resin composite structure is: (7).
[0029] Furthermore, the mechanical combination model in S4 is a series model; calculating the overall equivalent elastic modulus through the mechanical combination model includes: considering the iron core matrix, the interface transition layer, and the epoxy resin insulating varnish layer as series spring units; and calculating the longitudinal equivalent elastic modulus of the composite structure based on the equivalent elastic modulus and volume fraction of each layer according to the principle of series stiffness synthesis. The stiffness of the series spring unit is determined according to the equivalent elastic modulus, cross-sectional area, and length of each layer.
[0030] Specifically, the implementation process of this embodiment includes: Due to the fixing effect at both ends of the iron core, magnetostriction also causes an effect in the stacking direction of the iron core. The load is transmitted along the interlayer, and each layer bears the load sequentially, which can be regarded as a series model. Similarly, the equivalent series stiffness and longitudinal equivalent elastic modulus of the composite structure are: (8); (9).
[0031] An electronic device, the electronic device comprising: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure.
[0032] A computer storage medium storing computer program instructions, which, when executed by a processor, implement a method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure.
[0033] This embodiment provides a method for calculating the equivalent elastic modulus of an ultrathin silicon steel core and insulating varnish composite structure. It is applicable to the evaluation and optimization design of the mechanical properties of composite structures under different layered structures, interface characteristics and curing processes. This method can be executed by a composite structure equivalent modulus calculation device, which can be implemented in hardware and / or software and can be configured in a computer device.
[0034] This invention discloses a method for calculating the equivalent elastic modulus of an ultra-thin silicon steel core and insulating varnish composite structure. By calculating and correcting the equivalent elastic modulus of the core matrix, epoxy resin layer, and interface transition layer separately, and combining them in series or parallel according to the actual load direction, the method achieves accurate calculation of the equivalent elastic modulus of the ultra-thin silicon steel core and insulating varnish composite structure. This method effectively overcomes the shortcomings of traditional methods that ignore material orthogonal anisotropy, curing shrinkage effect, and interface damage, enabling the calculation results to more realistically reflect the macroscopic mechanical behavior of the composite structure under actual working conditions. The accurate equivalent elastic modulus parameters obtained thus provide a reliable mechanical basis for the vibration characteristic analysis and vibration reduction and noise reduction optimization design of power transformer cores, helping to suppress transformer operating noise from the source.
[0035] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for calculating the equivalent elastic modulus of an ultrathin silicon steel core and insulating varnish composite structure, characterized in that, include: S1. Obtain the equivalent elastic modulus of the iron core matrix; S2. Obtain the equivalent elastic modulus of the epoxy resin insulating varnish layer; S3. Obtain the equivalent elastic modulus of the interface transition layer between the iron core matrix and the epoxy resin insulating varnish layer. S4. Based on the equivalent elastic modulus of the core matrix, the epoxy resin insulating varnish layer and the interface transition layer, the overall equivalent elastic modulus of the composite structure is calculated through a mechanical combination model.
2. The method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in claim 1, characterized in that, The equivalent elastic modulus of the core matrix obtained in S1 includes: Based on the orthogonal anisotropy of the core matrix, its compliance coefficient is established; X-ray diffraction is used to obtain the grain orientation data of the silicon steel sheet and calculate the orientation distribution function; the Voigt-Reuss-Hill averaging method is used, combined with the orientation distribution function, to calculate the equivalent elastic modulus of the core matrix in the rolling direction and transverse direction, and its orthogonal anisotropic elastic modulus tensor is constructed.
3. The method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in claim 1, characterized in that, The equivalent elastic modulus of the epoxy resin insulating varnish layer obtained in step S2 includes: The initial elastic modulus of the epoxy resin insulating varnish in the glassy state was obtained through dynamic mechanical analysis; its curing shrinkage strain was measured through thermomechanical analysis; based on the initial elastic modulus and the curing shrinkage strain, the Voigt-Reuss-Hill model was modified to obtain the modified equivalent elastic modulus of the epoxy resin layer.
4. The method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in claim 1, characterized in that, The equivalent elastic modulus of the interface transition layer between the core matrix and the epoxy resin insulating varnish layer obtained in S3 includes: The actual bonding area ratio of the interface transition layer and the local elastic modulus obtained by nanoindentation test are obtained; the interface bonding strength data are obtained by shear test, and the interface damage factor is obtained by fitting based on the data; the effective elastic modulus of the interface transition layer is calculated using the actual bonding area ratio, the local elastic modulus and the interface damage factor.
5. The method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in claim 1, characterized in that, The mechanical combination model in S4 is a parallel model; the calculation of the overall equivalent elastic modulus through the mechanical combination model includes: regarding the iron core matrix, the interface transition layer and the epoxy resin insulating varnish layer as parallel spring units; and calculating the transverse equivalent elastic modulus of the composite structure based on the equivalent elastic modulus and volume fraction of each layer according to the principle of parallel stiffness superposition.
6. The method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in claim 5, characterized in that, The stiffness of the parallel spring unit is determined based on the equivalent elastic modulus, cross-sectional area, and length of each layer.
7. The method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in claim 1, characterized in that, The mechanical combination model in S4 is a series model; the calculation of the overall equivalent elastic modulus through the mechanical combination model includes: considering the iron core matrix, the interface transition layer and the epoxy resin insulating varnish layer as series spring units; and calculating the longitudinal equivalent elastic modulus of the composite structure based on the equivalent elastic modulus and volume fraction of each layer according to the principle of series stiffness synthesis.
8. The method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in claim 7, characterized in that, The stiffness of the series spring unit is determined based on the equivalent elastic modulus, cross-sectional area, and length of each layer.
9. An electronic device, characterized in that, The electronic device includes: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in any one of claims 1-8.
10. A computer storage medium, characterized in that, The computer storage medium stores computer program instructions, which, when executed by a processor, implement the method for calculating the equivalent elastic modulus of the ultrathin silicon steel core and insulating varnish composite structure as described in any one of claims 1-8.